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GATE 2024 PH – Question 5

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.

If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?

  1. 3/8
  2. 1/8
  3. 1/16
  4. 3/16

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Show answer and explanation

Correct answer: (D) 3/16

Explanation

Each long die has four equally likely faces: 2, 3, 5 and 7. For two dice there are $4\times4=16$ equally likely outcomes.

**Sum greater than 11 (that is, 12 or more).**
- $5+7=12$ ✓
- $7+5=12$ ✓
- $7+7=14$ ✓
- The other pairs give at most 10 (for example $3+7=10$ and $5+5=10$).

So 3 of the 16 outcomes qualify:
$$P=\frac3{16}\quad(\text{option D}).$$